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Find the direction cosines of the vector \(4i - 3j\).

Further Mathematics
WAEC 2010

Find the direction cosines of the vector \(4i - 3j\).

  • A. \(\frac{9}{10}, \frac{27}{10}\)
  • B. \(\frac{17}{27}, -\frac{17}{27}\)
  • C. \(\frac{4}{5}, -\frac{3}{5}\)
  • D. \(\frac{4}{7}, \frac{-3}{7}\)
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Correct Answer: Option C
Explanation

Given \(V = xi +yj\), the direction cosines are \(\frac{x}{|V|}, \frac{y}{|V|}\).

\(|4i - 3j| = \sqrt{4^{2} + (-3)^{2}} = \sqrt{25} = 5\)

Direction cosines = \(\frac{4}{5}, \frac{-3}{5}\).


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